SOLUTION: # 1.) The weight of full boxes of frosted Mini-wheat cereal are normally distributed with a standard deviation of 0.52 oz. A sample of 18 randomly selected boxes produced a mean we

Question 314396: # 1.) The weight of full boxes of frosted Mini-wheat cereal are normally distributed with a standard deviation of 0.52 oz. A sample of 18 randomly selected boxes produced a mean weight of 24.3 oz. Find the 95% confidence interval for the true mean weight of a box of this cereal.
# 2.) We are interested in estimating the mean life of a new product. How large a sample do we need to take in order to estimate the mean to within 0.20 of a standard deviation with 90% confidence?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
# 1.) The weight of full boxes of frosted Mini-wheat cereal are normally distributed with a standard deviation of 0.52 oz. A sample of 18 randomly selected boxes produced a mean weight of 24.3 oz. Find the 95% confidence interval for the true mean weight of a box of this cereal.
------------
sample mean: 24.3
E = [invT(0.975 with df = 17)]*0.52/sqrt(18) = 2.1098*0.1226 = 0.2586
------------
95% CI: 24.3-0.2596 < u < 24.3+0.2596
==========================================

# 2.) We are interested in estimating the mean life of a new product. How large a sample do we need to take in order to estimate the mean to within 0.20 of a standard deviation with 90% confidence?
-----------------
n = [z*s/E]^2
n = [1.645*s/0.2]^2
---
Note: You need to know the standard deviation.
=================================================
Cheers,
Stan H.

RELATED QUESTIONS
Suppose that the weight of cereal in boxes is labeled to have 20 oz is distributed with... (answered by rothauserc)

Suppose the weight of cereal in a box is labeled to contain 20 oz and is distributed with (answered by stanbon)

The mean weight of a box of cereal filled by a machine is 15.0 ounces, with a standard... (answered by stanbon)

suppose the mean weight of 32 ounce box of cereal is normally distributed with a mean of... (answered by Boreal)

Boxes of a certain cereal say they hold 15 oz. To make sure they do, the... (answered by Theo)

The weight of oranges growing in an orchard is normally distributed with a mean weight of (answered by Boreal)

A package of Toys Galore Cereal is marked "Net Wt. 12 oz." The actual weight is normally... (answered by Boreal)

Suppose a company repacks cereal with the use of a machine that is calibrated so that the (answered by CPhill)

The mean weight of a box of cereal filled by a machine is 16.0 ounces, with a standard... (answered by Theo)